The spatial fourth-order compact splitting FDTD scheme with modified energy-conserved identity for two-dimensional Lorentz model

Abstract In this paper, we give the energy conservation for the electromagnetic fields propagating in two-dimensional Lorentz media and develop a new spatial fourth-order compact splitting FDTD scheme to solve the two-dimensional electromagnetic Lorentz system. The spatial compact finite difference technique and the splitting technique are combined to construct the numerical scheme. The advantages of the developed scheme lie in its fourth-order accuracy in space and second-order accuracy in time, modified discrete energy conservation, unconditional stability as well as its easy implementation. These results are demonstrated rigorously in the paper. Numerical dissipation and numerical dispersion analysis are shown and numerical dispersion errors are compared with other schemes. Besides, numerical tests verify the modified discrete energy conservation and convergence ratios in time and space.

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